Properties

Label 8670m
Number of curves $1$
Conductor $8670$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 8670m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8670.m1 8670m1 \([1, 0, 1, -14023, 1512746]\) \(-43713001/116640\) \(-813652347918240\) \([]\) \(36720\) \(1.5485\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 8670m1 has rank \(0\).

Complex multiplication

The elliptic curves in class 8670m do not have complex multiplication.

Modular form 8670.2.a.m

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} + q^{7} - q^{8} + q^{9} - q^{10} + q^{11} + q^{12} + 3 q^{13} - q^{14} + q^{15} + q^{16} - q^{18} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display